Vectors Multiplication

Physics697

Actually I have two questions

1. The problem statement, all variables and given/known data

Vectors A and B are shown on the figure below. Which one of the
following statements is correct?
a) A . B = 0 and A × B ≠ 0
b) A . B ≠ 0 and A × B = 0
c) A . B ≠ 0 and A × B ≠ 0
d) A . B = 0 and A × B = 0
Picture: http://i.imgur.com/X0GB9.png

2. Relevant equations

A.B = AxBx + AyBy

3. The attempt at a solution

Obviously, the answer is zero. but the problem is the difference between A . B and A x B. I have long thought that those two are the same, but this question confused me.
I tried google for a bit and found out that [ dot product (u . v) gives a scalar ] and [ cross product (u x v) gives a pseudovector ]. It's my first time hearing about a pseudovector =_=

My second question is also about Vectors Multiplication

1. The problem statement, all variables and given/known data

A and B are the two vectors shown in the figure. Vector A is along the positive x
axis and has a magnitude of 5 cm, and the vector B is in the x-y plane at an angle 30º
with the positive x axis and has a magnitude of 4 cm. A × B =

a) 20 cm2 in the +x direction b) 10 cm2 in the +y direction
c) 10 cm2 in the +z direction d) 20 cm2 in the -y direction


2. Relevant equations

A.B = AxBx + AyBy

3. The attempt at a solution

When I tried to solve it I got C= 17.5 + 0, so the answer might be a.

This cm^2 and the +z confused me, so I just wanted to confirm.

256bits

Here is a re-fresher on dot and cross product.
http://ltcconline.net/greenl/courses...rs/dotcros.htm

For 2 vectors A and B orthoganol ( at right angles) then the dot product A . B = 0, (ie there is no component of A is the same direction as B ( or visa-versa ) sometimes called the projection of A on B.

But, the other part of the answer is A x B = 0 or A x B ≠ 0.

What is your relevant equation for A x B??

Well, you are multiplying a value in A with dimensions cm by one in B of dimension cm, so that would be cm^2.

Axis x and y make a plane,
Add another axis called z and you can work with volumes.
The axis can also be labelled by the unit vectors i,j,k, which you might not have seen yet.

Physics697

Thank you for you reply,
Yeah, I understood the first one thanks to the website you posted.

first question answer: a) A . B = 0 and A × B ≠ 0
and the answer for the second one is ' C= 17.5 + 0 '

Thanks (*